[90] | 1 | #include <stdio.h> |
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[89] | 2 | #include <math.h> |
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[90] | 3 | #include <malloc.h> |
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[89] | 4 | #define ROTATE(a,i,j,k,l) g=a[i][j];h=a[k][l];a[i][j]=g-s*(h+g*tau);\ |
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| 5 | a[k][l]=h+s*(g-h*tau); |
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| 6 | |
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| 7 | /* |
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| 8 | Computes all eigenvalues and eigenvectors of a real symmetric matrix a[1..n][1..n]. On |
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| 9 | output, elements of a above the diagonal are destroyed. d[1..n] returns the eigenvalues of a. |
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| 10 | v[1..n][1..n] is a matrix whose columns contain, on output, the normalized eigenvectors of |
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| 11 | a. nrot returns the number of Jacobi rotations that were required. |
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| 12 | */ |
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| 13 | void jacobi(float **a, int n, float d[], float **v, int *nrot) |
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| 14 | { |
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| 15 | int j,iq,ip,i; |
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[90] | 16 | float tresh,theta,tau,sm,s,h,g,c,*b,*z; |
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| 17 | float t; |
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| 18 | b = (float *) malloc(n * sizeof(float)); |
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| 19 | z = (float *) malloc(n * sizeof(float)); |
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[89] | 20 | |
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[90] | 21 | printf("in jacobi\n"); |
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| 22 | |
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| 23 | for (ip=0;ip<n;ip++) { // Initialize to the identity matrix. |
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| 24 | for (iq=0;iq<n;iq++) |
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| 25 | v[ip][iq]=0.0; |
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| 26 | v[ip][ip]=1.0; |
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[89] | 27 | } |
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[90] | 28 | printf("in jacobi 2\n"); |
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| 29 | for (ip=0;ip<n;ip++) { // Initialize b and d to the diagonal of a. |
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| 30 | b[ip]=d[ip]=a[ip][ip]; |
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| 31 | z[ip]=0.0; // This vector will accumulate terms of the form t*a[pq] as in equation (11.1.14). |
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[89] | 32 | } |
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| 33 | |
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[90] | 34 | printf("in jacobi 2\n"); |
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[89] | 35 | *nrot=0; |
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| 36 | for (i=1;i<=50;i++) { |
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| 37 | sm=0.0; |
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[90] | 38 | for (ip=0;ip<n-1;ip++) { // Sum off-diagonal elements. |
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[89] | 39 | for (iq=ip+1;iq<n;iq++) |
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| 40 | sm += fabs(a[ip][iq]); |
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| 41 | } |
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[90] | 42 | if (sm == 0.0) { // The normal return, which relies on quadratic convergence to machine underflow. |
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| 43 | free(z); |
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| 44 | free(b); |
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[89] | 45 | return; |
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| 46 | } |
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| 47 | if (i < 4) |
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[90] | 48 | tresh=0.2*sm/(n*n); // ...on the first three sweeps. |
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[89] | 49 | else |
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[90] | 50 | tresh=0.0; // ...thereafter. |
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[89] | 51 | for (ip=0;ip<n-1;ip++) { |
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| 52 | for (iq=ip+1;iq<n;iq++) { |
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| 53 | g=100.0*fabs(a[ip][iq]); |
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[90] | 54 | if (i > 4 && (float)(fabs(d[ip])+g) == (float)fabs(d[ip]) // After four sweeps, skip the rotation if the off-diagonal element is small. |
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[89] | 55 | && (float)(fabs(d[iq])+g) == (float)fabs(d[iq])) |
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| 56 | a[ip][iq]=0.0; |
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| 57 | else if (fabs(a[ip][iq]) > tresh) { |
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| 58 | h=d[iq]-d[ip]; |
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| 59 | if ((float)(fabs(h)+g) == (float)fabs(h)) |
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[90] | 60 | t=(a[ip][iq])/h; // t = 1/(2*theta) |
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[89] | 61 | else { |
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[90] | 62 | theta=0.5*h/(a[ip][iq]); |
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[89] | 63 | t=1.0/(fabs(theta)+sqrt(1.0+theta*theta)); |
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| 64 | if (theta < 0.0) t = -t; |
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| 65 | } |
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| 66 | |
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| 67 | c=1.0/sqrt(1+t*t); |
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| 68 | s=t*c; |
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| 69 | tau=s/(1.0+c); |
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| 70 | h=t*a[ip][iq]; |
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| 71 | z[ip] -= h; |
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| 72 | z[iq] += h; |
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| 73 | d[ip] -= h; |
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| 74 | d[iq] += h; |
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| 75 | a[ip][iq]=0.0; |
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| 76 | |
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[90] | 77 | for (j=0;j<ip-1;j++) { // Case of rotations 1 <= j < p. |
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[89] | 78 | ROTATE(a,j,ip,j,iq) |
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[90] | 79 | } |
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| 80 | for (j=ip+1;j<iq-1;j++) { // Case of rotations p < j < q. |
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[89] | 81 | ROTATE(a,ip,j,j,iq) |
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| 82 | } |
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[90] | 83 | for (j=iq+1;j<n;j++) { // Case of rotations q < j <= n. |
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[89] | 84 | ROTATE(a,ip,j,iq,j) |
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| 85 | } |
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| 86 | for (j=0;j<n;j++) { |
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| 87 | ROTATE(v,j,ip,j,iq) |
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| 88 | } |
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| 89 | |
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| 90 | ++(*nrot); |
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| 91 | } |
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| 92 | } |
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| 93 | } |
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| 94 | |
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| 95 | for (ip=0;ip<n;ip++) { |
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| 96 | b[ip] += z[ip]; |
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[90] | 97 | d[ip]=b[ip]; // Update d with the sum of t*a[pq], |
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| 98 | z[ip]=0.0; // and reinitialize z. |
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[89] | 99 | } |
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| 100 | } |
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| 101 | |
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| 102 | printf("Too many iterations in routine jacobi\n"); |
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[90] | 103 | } |
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| 104 | |
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| 105 | int main(int argc, char * argv) |
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| 106 | { |
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| 107 | int n, i, j; |
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| 108 | float *d; |
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| 109 | float **a; |
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| 110 | float **v; |
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| 111 | int nrot = 0; |
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| 112 | |
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| 113 | FILE * f = fopen("mat.in", "r"); |
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| 114 | fscanf(f,"%d", &n); |
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| 115 | |
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| 116 | a = (float **)malloc(n * sizeof(float*)); |
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| 117 | for(i = 0; i < n; i++) |
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| 118 | a[i] = (float *)malloc(n * sizeof(float)); |
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| 119 | |
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| 120 | v = (float **)malloc(n * sizeof(float*)); |
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| 121 | for(i = 0; i < n; i++) |
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| 122 | v[i] = (float *)malloc(n * sizeof(float)); |
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| 123 | |
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| 124 | d = (float *)malloc(n * sizeof(float)); |
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| 125 | |
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| 126 | for(i = 0; i < n; i++) |
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| 127 | for(j = 0; j < n; j++) |
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| 128 | fscanf(f,"%f", &a[i][j]); |
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| 129 | for(i = 0; i < n; i++) |
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| 130 | { |
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| 131 | for(j = 0; j < n; j++) |
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| 132 | printf("%f ", a[i][j]); |
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| 133 | printf("\n"); |
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| 134 | } |
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| 135 | |
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| 136 | jacobi(a, n, d, v, &nrot); |
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| 137 | |
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| 138 | printf("v:\n"); |
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| 139 | for(i = 0; i < n; i++) |
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| 140 | { |
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| 141 | for(j = 0; j < n; j++) |
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| 142 | printf("%f ", v[i][j]); |
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| 143 | printf("\n"); |
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| 144 | } |
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| 145 | |
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| 146 | printf("d:\n"); |
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| 147 | for(i = 0; i < n; i++) |
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| 148 | { |
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| 149 | printf("%f ", d[i]); |
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| 150 | } |
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| 151 | |
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| 152 | return 0; |
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| 153 | } |
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| 154 | |
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